Question

If ‘$m$’ is the mass of a body, $'a'$ is a amplitude of vibration, and $'w'$ is angular frequency then $\;\dfrac{1}{2}m{a^2}{w^2}$ has same dimensional formula as:
(A) work
(B) moment of force
(C) energy
(D) all the above

Answer 1

Hint It should be known to us that the moment of force is defined as the measure of the amount of tendency to cause a rotation to a body about a specific point or we can axis. The formula for the moment of force is given as the multiplication between the distance from the applied force to the object and the applied force.

Complete step by step answer:
We know that the dimension of $\;\dfrac{1}{2}m{a^2}{w^2}$= $W{L^2}\left( {\dfrac{1}{{{T^2}}}} \right) = M{L^2}{T^{ - 2}}$
And that of work = $(force \times$distance) = $\left( {\dfrac{{ML}}{{{T^2}}}} \right) \times L = M{L^2}{Y^{ - 2}}$
So, the moment of force = $\overrightarrow{F} \times \overrightarrow{r} =\left[ {\dfrac{{ML}}{{{T^2}}}} \right] \times L = M{L^2}{Y^{ - 2}}$
As we know that energy = work = $M{L^2}{T^{ - 2}}$

Hence, the correct answer is Option D.

Note The term angular frequency is defined as the measure of the angular frequency displacement per unit of time. The unit is described as degree per second. It should be known to us that the angular velocity formula is the same as compared to the equation for the angular frequency.